Geodesic
Further Pieri-type formulas for the nonsymmetric Macdonald polynomial
Journal of Algebraic Combinatorics, Tome 36 (2012) no. 1, pp. 45-66.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The branching coefficients in the expansion of the elementary symmetric function multiplied by a symmetric Macdonald polynomial $P _{ \kappa }( z)$ are known explicitly. These formulas generalise the known $r=1$ case of the Pieri-type formulas for the nonsymmetric Macdonald polynomials $E _{ \eta }( z)$. In this paper, we extend beyond the case $r=1$ for the nonsymmetric Macdonald polynomials, giving the full generalisation of the Pieri-type formulas for symmetric Macdonald polynomials. The decomposition also allows the evaluation of the generalised binomial coefficients $\tbinom h$ n $_{ q, t} \tbinom{\eta }{\nu }$_q,t associated with the nonsymmetric Macdonald polynomials.
Keywords: keywords Macdonald polynomial, Pieri formulas, nonsymmetric, q-binomial coefficients 
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     author = {Baratta, W.},
     title = {Further {Pieri-type} formulas for the nonsymmetric {Macdonald} polynomial},
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Baratta, W. Further Pieri-type formulas for the nonsymmetric Macdonald polynomial. Journal of Algebraic Combinatorics, Tome 36 (2012) no. 1, pp. 45-66. http://geodesic.mathdoc.fr/item/JAC_2012__36_1_a5/